Problem: The grades on a physics midterm at Covington are normally distributed with $\mu = 77$ and $\sigma = 2.5$. Kevin earned a n $80$ on the exam. Find the z-score for Kevin's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Kevin's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{80 - {77}}{{2.5}}} $ ${ z \approx 1.20}$ The z-score is $1.20$. In other words, Kevin's score was $1.20$ standard deviations above the mean.